Not necessarily so, because...
It's why it's not recommended to 'try and make it sound really good on phone' (as your sole aim) or only aim, as for example phones may have a naturally more tinny sound, so you might dull the sound, only for the mix to sound really dull everywhere else.
As you highlighted, some devices or systems may have 'enhancements', or may just have different frequency responses -- for example, lets say the phone had scooped low mids, you may end up lifting the low mids so they're more audible and sound 'good' on the phone; but let's say Opium Dave is listening back on headphones that have a low mid push, that playback will sound horribly boxy and muddy --- getting it right on good/flat monitoring, the play back should land reasonably across the devices (as you would expect the usual response of each device, so tracks won't sound off)
Another key to getting this aspect of mixing right, is
cross referencing, where you would check your mix against typical playback devices, and make subtle adjustments to ensure the mix accounts for the potential pitfuls of other devices, in a way that does not negatively impact the mix as heard on flat/accurate devices.
What this may look like is... let's say on phone playback, the delay/reverb disappears, and the record loses a key 'feel', you can likely creep up the level of the delay/verb until it is audible enough on phone, but still sounds absolutely fine/good on flat/accurate monitoring. This can go for any element or frequency of the mix. Probably more familiar is the 'making bass audible on smaller speakers', where you can make the bass audible in a way that doesn't mess it up elsewhere.
